# Estimating the effects of a California gun control program with Multitask Gaussian Processes

**Authors:** Eli Ben-Michael, David Arbour, Avi Feller, Alex Franks, Steven Raphael  
**arXiv:** [2110.07006](https://arxiv.org/abs/2110.07006)  
**Date:** 2021-10-13  
**Summary page:** https://www.summarizepaper.com/en/paper/2110.07006v2/

## Key points

- Gun violence is a major public safety concern in the United States
- California implemented a firearm monitoring program called the Armed and Prohibited Persons System (APPS) in 2006 to address this issue
- The APPS program identifies firearm owners who become prohibited from owning one due to federal or state law and confiscates their firearms
- A study was conducted to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for years before and after the introduction of the program
- Researchers adapted a non-parametric Bayesian approach called multitask Gaussian Processes (MTGPs) to estimate the causal effect of APPS
- Increased monitoring and enforcement from the APPS program substantially decreased homicides in California, with no measurable effect on non-gun murder
- Estimated cost per murder avoided was substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort
- The MTGP framework is a promising approach for estimating causal effects with panel data more broadly, yielding coherent uncertainty quantification while producing uncertainty intervals that grow over time post-treatment.

## Summary

Gun violence is a major public safety concern in the United States, and California implemented a unique firearm monitoring program called the Armed and Prohibited Persons System (APPS) in 2006 to address this issue. The APPS program identifies firearm owners who become prohibited from owning one due to federal or state law and confiscates their firearms. This study aims to assess the effect of APPS on California murder rates using annual, state-level crime data across the US for years before and after the introduction of the program. To do so, researchers adapted a non-parametric Bayesian approach called multitask Gaussian Processes (MTGPs) to estimate the causal effect of APPS. The MTGP framework allows for flexible and parsimonious panel data models that nest many existing approaches while allowing direct control over both dependence across time and units, as well as natural uncertainty quantification. The approach was extended to incorporate non-Normal outcomes, auxiliary covariates, and multiple outcome series, which are all important in this application. Applying this approach revealed that increased monitoring and enforcement from the APPS program substantially decreased homicides in California. The study found that the effect on murder was driven entirely by declines in gun-related murder with no measurable effect on non-gun murder. Estimated cost per murder avoided was substantially lower than conventional estimates of the value of a statistical life, suggesting a very high benefit-cost ratio for this enforcement effort. Methodologically, researchers believe that the MTGP framework is a promising approach for estimating causal effects with panel data more broadly. The Bayesian approach yields coherent uncertainty quantification while producing uncertainty intervals that grow over time post-treatment. This study is one of few papers specifically using GPs to estimate causal effects in panel data settings. While there are other relevant proposals such as Modi and Seljak's GP approach for estimating causal effects in frequency domain or Carlson's GP approach without exploiting multitask structure, researchers view their model as complementary to these approaches. Overall, this study provides a detailed analysis of the impact of APPS on California murder rates and demonstrates the potential of MTGPs for estimating causal effects with panel data.